Allow me to clarify, re: waivers vs. re-entry waivers.
When you put a player on waivers, other teams have 24 hours to put in a claim. A player who is claimed becomes the property of the claiming team, and the team who waived him is entirely done with him.
A player who goes unclaimed can, if the organization desires, remain with the team (with his salary staying on the books and counting against the caps), OR be assigned to the minor-league affiliate (with his salary staying on the books but not counting against the cap), OR (and this is a new option, really) he can head to the KHL, with either the KHL team taking on his salary or him being suspended (in either case, the NHL team maintains his rights for the life of the contract but doesn't pay him or have his salary count against the cap).
Often times -- and this is something that many people don't seem to understand -- players who are waived are in fact retained with the NHL club (Khabibulin being a good instance) and, from the outside, it looks like nothing has really happened. Life continues on as usual for the player and the team. The organization has tried to give away a player, but no one is interested in picking him up. After this point, the organization has, I believe, 9 games or 28 days (whichever comes first) to demote him, if that's what it wants to do. If the player remains with the team after that time has elapsed, then the waiver window has closed. If the team wanted to demote him to the minors after that time, it would have to pass him through waivers again.
Re-entry waivers are an entirely different beast, and the big mistake people have been making around here is in thinking that, once you are waived, you have to pass through re-entry waivers to play again. This is simply
not the case, and the reality is much more complicated. A player who is waived can be, as I said, assigned to the minor-league affiliate. This is the crucial factor: the moment an organization assigns a player to the minors is the moment when re-entry waivers come into play. If, after that assignment, the organization wants to recall that player from the minors, it has to pass him through re-entry waivers -- at which point, as we all know, he can be claimed by other teams at half price, with the original organization being left on the hook for the other half of the player's salary.
We need a section of this site dedicated to stuff cap-, CBA-, and rule-related. This is, like, the 4th time I've found myself explaining this point.